- There are 40 students in a class. 26students like to read mathematics and 23 students
like to read English. Find the number of students who like to read both subjects.

Answer:

Option D vertical angles is your answer ☺️☺️

Answer:

Vertical angles

Step-by-step explanation:

∠WTU and ∠STZ are opposite each other; hence they are vertical angles.

The average is 40 and  the margin of error is 10.95.

What is margin of error?

The margin of error is a statistic expressing the amount of random sampling in the result of a survey.

Average (A) = sum of all the value/ given set.

A = (51+ 41 + 28)/3 = 40

margin of error = 100/square root of 120 = 10.95.

Therefore, the average is 40 and  the margin of error is 10.95.

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Answer 1 is correct.

Part A: Student B's mistake was using the wrong formula in Step 2. Instead of using the formula for the sum of squares of sine and cosine, they used the formula for the sum of squares of tangent and cotangent. This led them to an incorrect expression in Step 3.

Part B: The correct simplification for student B is:

(1 + tan^2 θ) / cot θ

Substitute 1 + tan^2 θ with sin^2 θ / cos^2 θ + cos^2 θ / sin^2 θ:

(sin^2 θ / cos^2 θ + cos^2 θ / sin^2 θ) / cot θ

Simplify the expression by multiplying the numerator by sin^2 θ and the denominator by cos^2 θ:

(sin^4 θ + cos^4 θ) / (sin^2 θ cos^2 θ)

Simplify the numerator:

[(sin^2 θ + cos^2 θ)^2 - 2 sin^2 θ cos^2 θ] / (sin^2 θ cos^2 θ)

= (1 - 2 sin^2 θ cos^2 θ) / (sin^2 θ cos^2 θ)

Substitute cot^2 θ = 1 + tan^2 θ:

(1 + tan^2 θ - 2) / (sin^2 θ cos^2 θ)

= (tan^2 θ - 1) / (sin^2 θ cos^2 θ)

Simplify the numerator:

= -(1 - tan^2 θ) / (sin^2 θ cos^2 θ)

= -csc^2 θ / cot^2 θ

Flip the denominator and change division to multiplication:

= -csc^2 θ * tan^2 θ / (sin^2 θ)

Substitute sin^2 θ = 1 - cos^2 θ:

= -csc^2 θ * tan^2 θ / (1 - cos^2 θ)

Substitute cos^2 θ = 1 - sin^2 θ:

= -csc^2 θ * tan^2 θ / (sin^2 θ)

Simplify the expression:

= -1 / sin^2 θ

= -csc^2 θ

Therefore, the correct simplification for student B is -csc^2 θ.

Answer:

I do not understand the question please ask a question before sending that

Answer:

yes

Step-by-step explanation:

its correct because divide by 2/ 28/16=14/8

maybe

1. The trigonometric ratios are given as follows:

2. The equation to solve for x is given as follows: sin(52º) = x/13.

3. Two equations to solve for m are given as follows:

4. The length of the hypotenuse of the triangle is given as follows: 7.9 inches.

5. The lengths are given as follows:

The three trigonometric ratios are given as follows:

In the second problem, we have that the side x is opposite to the angle of 52º, while the hypotenuse is of 13, hence the equation to solve for x is given as follows:

sin(52º) = x/13.

In item 3, the Pythagorean Theorem is used to solve for m, as follows:

n² + m² = l².

m² = l² - n²

m = square root (l² - n²).

In item 4, we have that the angle opposite to the leg of length 7 inches is of 62º, hence the hypotenuse is given as follows:

sin(62º) = 7/h

h = 7/sin(62º)

h = 7.9 inches.

The length BD in item 5 is obtained as follows:

cos(30º) = BD/5

BD = 5 x cos (30º)

BD = 4.3 cm.

Then the length BC is calculated as follows:

sin(22º) = 4.3/BC

BC = 4.3/sin(22º)

BC = 11.5 cm.

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The probability that 2 or fewer in the sample will favor the project is  4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%

According to the question,

It is given that according to the student's government

The probability that number of students in favor of increment in fees : p = 0.70

The probability that number of students against the increment : q = 0.30

Sample Size : n = 12

Number of students follows Binomial distribution

(a) We have to find the probability that 2 or fewer in the sample will favor the project

P( x ≤ 2) = P(0) + P(1) + P(2)

As we know ,

P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾

=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰

=>  P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹  + 12×11/2 × (0.70)²(0.30)¹⁰

=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]

=>  P( x ≤ 2) = 5.9×10⁻⁶[0.78]

=>  P( x ≤ 2) = 4.368 × 10⁻⁶

Which is very close to zero

(b) The data doesn't support the student government claim.

The data seem to indicate that the percent favoring the increase in fees is less than 70%.

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The nature of the research is called Observational Study while the target Population is American Students.

1) In study, we survey members of a sample without trying to affect them while in experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive treatment. Thus, this is an observational study.

2) The sample is the 100 students made up of 50 boys and 50 girls.

3) The target Population are American College Students

4) The sampling method is; Simple random Sampling

5) The data is qualitative because it deals with description of feelings rather than dealing with numbers and figures.

6) It is unlikely that the results would be invalid because of sampling bias as it was only done in a private university.

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Answer:

3.5?

Step-by-step explanation:

sorry that's all i can do..

Answer: 3.5714286e^-10 or 0.00000000035714286 or 3.5714286 × 10^-10

Step-by-step explanation:

First, we divide 0.0001 by 28, which equals 3.5714286e-6.

And since we added 4 zeros to the equation, the negative (e) will be pushed by -4. So, it should look like this: 3.5714286e-10, and the equation is complete.

The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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Answer:

28

Step-by-step explanation:

p(x)=-2(x-9)^2+100

Let x= 15

p(15)=-2(15-9)^2+100

Parentheses first

      = -2 ( 6) ^2 + 100

Then exponents

     = -2 * 36 + 100

Then multiply

    = -72 + 100

Then add

   =28

Answer:

324

Step-by-step explanation:

f(×)=18f (x)

f (x)=18×18

f1l (18)=324

Answer:

5

Step-by-step explanation:

10/2=5

The scale factor of the given case that the distance from D to D' is 10 and the distance from A to D is 2 will be 5.

What is the scale factor?

The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics.

The scale factor is the ratio between two big and small figures and the ratio is called a scale for the given geometry.

For example, if we have a triangle with a side of 10 meters and another triangle with a side of 5 then the scale ratio will be 10/5 = 2.

Given that

distance from D to D' is 10

distance from A to D is 2  

So the scale ratio will be

DD'/AD  = 10/2  = 5 hence scale ratio will be 5 for the given

geometry.

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Answer:

Step-by-step explanation:

First, let's find x:-

(15x-2)° = (9x+10)°

15x-2 = 9x+10

6x = 12

x = 2°

Now, let's find y:-

28 + y° = 180°

y = 180-28

y = 150°

______________________

Hope this helps you!

Have a great day!

she could buy atleast 8, 15 dollar video games

Step-by-step explanation:

240 -120(for her bank)

then you'll b left w 120

divide 120 by 15 and get 8

Answer:

y = 3x

Step-by-step explanation:

A proportional function has the equation

y = kx, where k is the constant of proportionality and also the slope of the line.

Answer: y = 3x

The equation that represents the line whose slope of proportional relationship is 3 is; y = 3x.

The slope of the proportional relationship as given is 3.

However, the equation of the line which represents a proportional relationship usually takes the form; y = Mx.

Since, slope, m = 3.

The equation of the line is; y = 3x.

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Answer:

b = 3

Step-by-step explanation:

(2,5) is information! x = 2 and y = 5.

Use these values in the equation:

y = x + b

5 = 2 + b

Subtract 2.

3 = b

The equation of the line is y = x + 3.

The required property justifies the step is an addition property of equality.

What is mathematical property?

The rules governing how numbers relate to and interact with one another are known as mathematical properties. There are four fundamental properties. i.e. distributive, addition, commutative and subtraction.

Given, 2x +3 = -5x -1

Applying addition property of equality,

Adding 5x to both sides, we get

7x + 3 = -1

Hence, the required property justifies the step is an addition property of equality.

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By applying the Theorem of Intersecting Secant, the measure of angle WT is equal to 51°.

By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the Theorem of Intersecting Secants.

The Theorem of Intersecting Secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the Theorem of Intersecting Secant, angle P will be given by this formula:

m<P = ½ × (m<RS - m<WT)

Substituting the given parameters into the formula, we have;

35 = ½ × (121 - m<WT)

70 = 121 - m<WT

m<WT = 121 - 70

m<WT = 51°.

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Answer:

x 64 3pk1

Step-by-step explanation:

The equation of the Parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

The vertex form of a parabola is given by:y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We are given that the vertex is (4, -2), so we can substitute these values in the equation to get:y = a(x - 4)^2 - 2

Now, we need to find the value of "a". To do this, we can use the fact that the y-intercept is (0, -66). Since the point (0, -66) lies on the parabola, we can substitute x = 0 and y = -66 in the equation above to get:-66 = a(0 - 4)^2 - 2

Simplifying this, we get:-66 = 16a - 2

Adding 2 to both sides, we get:-64 = 16a

Dividing both sides by 16, we get:a = -4

Substituting this value of "a" in the equation above, we get the equation of the parabola in vertex form:y = -4(x - 4)^2 - 2

Therefore, the equation of the parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

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One can be able to  test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:

Digital Construction is known to be a term that connote  the act of using digital technologies to be able to make construction to be more better and  with higher quality.

Note that  a lot of the new technologies have been seen to have proven themselves and gives  a lot of opportunities for the construction,

In the use of the digital tools, one can Construct a line or a line segment and then uses the move tool to drag some points around, and then watch to see what happens.

Therefore,  One can be able to  test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:

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Answer:

coefficient because they are not the same so they can not be constant because it is not the same in every week

The explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

The explicit formula for the given sequence is:

a_n = 100n + 12

In the given sequence, each term is obtained by adding 100 to the previous term. The first term is 12, and each subsequent term is obtained by adding 100 to the previous term.

Using the formula, we can calculate any term in the sequence by substituting the corresponding value of n. For example:

a_1 = 100(1) + 12 = 112

a_2 = 100(2) + 12 = 212

a_3 = 100(3) + 12 = 312

a_4 = 100(4) + 12 = 412

Therefore, the explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

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Answer:

Options (1), (2), (3) and (7)

Step-by-step explanation:

Given expression is \(\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}\).

Now we will solve this expression with the help of law of exponents.

\(\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}=\frac{\sqrt[3]{(2^3)^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}\)

           \(=\frac{\sqrt[3]{2\times 3} }{3\times2^{\frac{1}{9}}}\)

           \(=\frac{2^{\frac{1}{3}}\times 3^{\frac{1}{3}}}{3\times 2^{\frac{1}{9}}}\)

           \(=2^{\frac{1}{3}}\times 3^{\frac{1}{3}}\times 2^{-\frac{1}{9}}\times 3^{-1}\)

           \(=2^{\frac{1}{3}-\frac{1}{9}}\times 3^{\frac{1}{3}-1}\)

           \(=2^{\frac{3-1}{9}}\times 3^{\frac{1-3}{3}}\)

           \(=2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }\) [Option 2]

\(2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2\) [Option 1]

\(2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2\)

                \(=(2^2)^{\frac{1}{9}}\times (3^2)^{-\frac{1}{3} }\)

                \(=\sqrt[9]{4}\times \sqrt[3]{\frac{1}{9} }\) [Option 3]

\(2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(2^2)^{\frac{1}{9}}\times (3^{-2})^{\frac{1}{3} }\)

               \(=\sqrt[9]{2^2}\times \sqrt[3]{3^{-2}}\) [Option 7]

Therefore, Options (1), (2), (3) and (7) are the correct options.

Using inequalities, Y(x=0) = -2 and X(y=0) = -2 in region 1.

To pick area 1, draw a line at the intersection of (-2,0) and (0, -2), then choose the right side. such as.

Region 2) To pick the region to the left or upwards in region 2, we must draw a line from (0,2) to (-2,4).

Y(x=0) = 2\sX(y=-2) = -4

Region 3) To pick the region to the right, we must draw a line connecting (-4,0) and (0,4), as I'll demonstrate.

Inequalities in mathematics describe the relationship between two non-equal numbers. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, several inequalities are utilised to compare the numbers, whether it is less than or higher than.

The feasible area is now visible. Let's determine the vertices' coordinates.

Where the blue and green lines intersect is our first vertex.

3x + 2 = x + 4 and y = 3x + 2

3x - x = 4 - 2

y = 3× (1) + 2 = 3 + 2 = 5 when 2x = 2x = 1

(X, Y) = Vertex 1 (1,5)

The intersection of the red and green lines is at vertex #2:

y = -x -2; y = x + 4; y = x + 4 = -x - 2; and y = x + x = -2 - 4

2x = -6, x = -6/2, and y = (-3) + 4 = -3 + 4 = 1 are the results.

(X, Y) = Vertex 2 (-3,1)

The intersection of the red and blue lines is at vertex 3:

y = -x - 2, y = 3x + 2 -x - 2, and y = 2 + 2 -4 x = 4 x = -4 / 4 = -1;

So, y = 3×(-1) + 2 = -3 + 2 = -1

(X, Y) = Vertex 3 (-1, -1)

Let's now modify the graph by including the supplied equation.

The intercept where Y=0 is 0 is given by f(x,y) = -3x + 5y = 0 5y = 3x + 0 y = 3/5 × X + 0

the gradient m = 3/5

A line can be drawn from (0,0) to (-10, -6)

Let's now examine how it would appear in the area where it is practical.

We can see that the function intercepts the blue line or the line of the second section, which is where the largest value is located.

y = 3x + 2 3x + 2 (3/5 - 3) x = 2 -12/5 × x = 2 x = -5/6.

Hence, y = 3x + 2 3/5 × (-5/6) = -1/2.

The maximum is therefore found at (x,y) = (-5/6, -1/2).

The point where the function crosses the red line now marks the minimum.

y = 3/5 × x; y = -x -2

3/5 x = -x - 2\s (3/5 + 1) × x = -2\s8/5 x = - 2\sx = -2× (5/8) = -5/4.

y = 3/5 × (-5/4) = -3/4

The minimum is thus found at (x,y) = (-5/4, -3/4)

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The integer form is + 40.

The integer form is - 25

An integer is a whole number from the set of negative, non-negative, and positive numbers.

Therefore, integers can be written without fractional components.

Hence, integers may include negative or positive numbers . Examples are -1, 2, 5, -8, 9 and many more.

A deposit of 40 dollars means gain. Therefore, the integer form is + 40.

A loss of 25 pounds mean loss. Therefore, the integer form is - 25

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-19.99; The line of best fit underpredicts the student's science test score.

So correct option is A.

A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.

The predicted science score for the student with IQ 100 can be calculated using the line of best fit:

ŷ = −20.3 + 0.7489 * 100 = 71.59

The residual is the difference between the actual science test score and the predicted science score:

residual = actual score - predicted score = 52.6 - 71.59 = -19.99

So the line of best fit underpredicts the student's science test score by 19.99 points.

Therefore, the residual is:

-19.99; The line of best fit underpredicts the student's science test score.

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Answer:

5 or -2

Step-by-step explanation:

|2x-3| can equal either (2x-3) or -(2x-3) thus

(2x-3) = 7

2x = 10

x = 5

-(2x-3) = 7

-2x = 4

x = -2

Answer: it’s 5 or -2, |2x-3| can equal either (2x-3) or -(2x-3) thus(2x-3) = 72x = 10x = 5-(2x-3) = 7-2x = 4x = -2

Step-by-step explanation: hope this helps0^0

Answer:

see below

Step-by-step explanation:

0.68923 round to nearest hundredth ​is 0.69